Whakaoti i te (1/2)200t^2=10000

$$( 1 / 2 ) 200 t ^ { 2 } = 10000$$

Whakaoti mō t

$$t=10$$

$$t=-10$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakareatia te \frac{1}{2} ki te 200, ka 100.

$$100t^{2}=10000$$

Tangohia te 10000 mai i ngā taha e rua.

$$100t^{2}-10000=0$$

Whakawehea ngā taha e rua ki te 100.

$$t^{2}-100=0$$

Whakaarohia te t^{2}-100. Tuhia anō te t^{2}-100 hei t^{2}-10^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(t-10\right)\left(t+10\right)=0$$

Hei kimi otinga whārite, me whakaoti te t-10=0 me te t+10=0.

$$t=10 t=-10$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te \frac{1}{2} ki te 200, ka 100.

$$100t^{2}=10000$$

Whakawehea ngā taha e rua ki te 100.

$$t^{2}=\frac{10000}{100}$$

Whakawehea te 10000 ki te 100, kia riro ko 100.

$$t^{2}=100$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$t=10 t=-10$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te \frac{1}{2} ki te 200, ka 100.

$$100t^{2}=10000$$

Tangohia te 10000 mai i ngā taha e rua.

$$100t^{2}-10000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 100 mō a, 0 mō b, me -10000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 100\left(-10000\right)}}{2\times 100}$$

Pūrua 0.

$$t=\frac{0±\sqrt{-4\times 100\left(-10000\right)}}{2\times 100}$$

Whakareatia -4 ki te 100.

$$t=\frac{0±\sqrt{-400\left(-10000\right)}}{2\times 100}$$

Whakareatia -400 ki te -10000.

$$t=\frac{0±\sqrt{4000000}}{2\times 100}$$

Tuhia te pūtakerua o te 4000000.

$$t=\frac{0±2000}{2\times 100}$$

Whakareatia 2 ki te 100.

$$t=\frac{0±2000}{200}$$

Nā, me whakaoti te whārite t=\frac{0±2000}{200} ina he tāpiri te ±. Whakawehe 2000 ki te 200.

$$t=10$$

Nā, me whakaoti te whārite t=\frac{0±2000}{200} ina he tango te ±. Whakawehe -2000 ki te 200.

$$t=-10$$

Kua oti te whārite te whakatau.

$$t=10 t=-10$$